8.1 Random 2-sat and Proof That R 2 = 1
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چکیده
Theorem 8.2 [CR92] The threshold r2 exists and is r2 = 1. Proof: We proved one direction of Theorem 8.2 in the last lecture, by showing that Pr[φ is satisfiable]→ 1 for r ≤ (1− ). We now prove the other direction. Assume m = (1 + )n. Define t = n. (We’ll see the reason for this choice later.) The approach we’ll take is to define a collection of sets of clauses that are not satisfiable, and then show that with high probability, some such set appears in φ.
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